Local Number Field Search Results

Degree		Discriminant exponent $c$		Galois group
Prime $p$		Ramification index $e$		Top slope

Results (displaying all 47 matches)

Label	Polynomial	$p$	$e$	$f$	$c$	Galois group	Slope content
2.6.0.1	x^6 - x + 1	2	1	6	0	$C_6$ (as 6T1)	$ [\ ]^{6}$
2.6.4.1	x^6 + 3x^5 + 6x^4 + 3x^3 + 9x + 9	2	3	2	4	$S_3$ (as 6T2)	$ [\ ]_{3}^{2}$
2.6.4.2	x^6 - 2x^3 + 4	2	3	2	4	$S_3\times C_3$ (as 6T5)	$ [\ ]_{3}^{6}$
2.6.6.1	x^6 + x^2 - 1	2	2	3	6	$A_4$ (as 6T4)	$ [2, 2]^{3}$
2.6.6.2	x^6 - x^4 - 5	2	2	3	6	$A_4\times C_2$ (as 6T6)	$ [2, 2]^{6}$
2.6.6.3	x^6 + 2x^4 + x^2 - 7	2	2	3	6	$C_6$ (as 6T1)	$ [2]^{3}$
2.6.6.4	x^6 + x^2 + 1	2	2	3	6	$A_4\times C_2$ (as 6T6)	$ [2, 2, 2]^{3}$
2.6.6.5	x^6 - 2x^4 + x^2 - 3	2	2	3	6	$C_6$ (as 6T1)	$ [2]^{3}$
2.6.6.6	x^6 - 13x^4 + 7x^2 - 3	2	2	3	6	$A_4\times C_2$ (as 6T6)	$ [2, 2, 2]^{3}$
2.6.6.7	x^6 + 2x^2 + 2x + 2	2	6	1	6	$S_4$ (as 6T7)	$ [4/3, 4/3]_{3}^{2}$
2.6.6.8	x^6 + 2x + 2	2	6	1	6	$S_4$ (as 6T8)	$ [4/3, 4/3]_{3}^{2}$
2.6.8.1	x^6 + 2x^3 + 2	2	6	1	8	$D_{6}$ (as 6T3)	$ [2]_{3}^{2}$
2.6.8.2	x^6 + 2x^3 + 2x^2 + 6	2	6	1	8	$S_4\times C_2$ (as 6T11)	$ [4/3, 4/3, 2]_{3}^{2}$
2.6.8.3	x^6 + 2x^3 + 6	2	6	1	8	$D_{6}$ (as 6T3)	$ [2]_{3}^{2}$
2.6.8.4	x^6 + 2x^3 + 2x^2 + 2	2	6	1	8	$S_4\times C_2$ (as 6T11)	$ [4/3, 4/3, 2]_{3}^{2}$
2.6.9.1	x^6 + 4x^4 + 4x^2 - 8	2	2	3	9	$C_6$ (as 6T1)	$ [3]^{3}$
2.6.9.2	x^6 + 4x^2 - 8	2	2	3	9	$A_4\times C_2$ (as 6T6)	$ [2, 2, 3]^{3}$
2.6.9.3	x^6 - 4x^4 + 4x^2 + 24	2	2	3	9	$C_6$ (as 6T1)	$ [3]^{3}$
2.6.9.4	x^6 + 4x^2 + 24	2	2	3	9	$A_4\times C_2$ (as 6T6)	$ [2, 2, 3]^{3}$
2.6.9.5	x^6 - 4x^4 + 4x^2 + 8	2	2	3	9	$C_6$ (as 6T1)	$ [3]^{3}$
2.6.9.6	x^6 + 4x^2 + 8	2	2	3	9	$A_4\times C_2$ (as 6T6)	$ [2, 2, 3]^{3}$
2.6.9.7	x^6 + 4x^4 + 4x^2 - 24	2	2	3	9	$C_6$ (as 6T1)	$ [3]^{3}$
2.6.9.8	x^6 + 4x^2 - 24	2	2	3	9	$A_4\times C_2$ (as 6T6)	$ [2, 2, 3]^{3}$
2.6.10.1	x^6 + 2x^5 + 2x^4 + 2	2	6	1	10	$S_4$ (as 6T7)	$ [8/3, 8/3]_{3}^{2}$
2.6.10.2	x^6 + 2x^5 + 2x^4 + 2x^2 + 2	2	6	1	10	$S_4$ (as 6T7)	$ [8/3, 8/3]_{3}^{2}$
2.6.10.3	x^6 + 2x^5 + 4x + 2	2	6	1	10	$S_4$ (as 6T8)	$ [8/3, 8/3]_{3}^{2}$
2.6.10.4	x^6 + 2x^5 + 2x^4 + 6	2	6	1	10	$S_4$ (as 6T8)	$ [8/3, 8/3]_{3}^{2}$
2.6.10.5	x^6 + 2x^5 + 6	2	6	1	10	$S_4\times C_2$ (as 6T11)	$ [2, 8/3, 8/3]_{3}^{2}$
2.6.10.6	x^6 + 2x^5 + 4x^3 + 6	2	6	1	10	$S_4\times C_2$ (as 6T11)	$ [2, 8/3, 8/3]_{3}^{2}$
2.6.10.7	x^6 + 2x^5 + 4x^3 + 2	2	6	1	10	$S_4\times C_2$ (as 6T11)	$ [2, 8/3, 8/3]_{3}^{2}$
2.6.10.8	x^6 + 2x^5 + 2	2	6	1	10	$S_4\times C_2$ (as 6T11)	$ [2, 8/3, 8/3]_{3}^{2}$
2.6.11.1	x^6 + 14	2	6	1	11	$D_{6}$ (as 6T3)	$ [3]_{3}^{2}$
2.6.11.10	x^6 + 2x^4 + 2	2	6	1	11	$S_4\times C_2$ (as 6T11)	$ [4/3, 4/3, 3]_{3}^{2}$
2.6.11.11	x^6 + 2x^4 + 2x^2 + 2	2	6	1	11	$S_4\times C_2$ (as 6T11)	$ [8/3, 8/3, 3]_{3}^{2}$
2.6.11.12	x^6 + 2x^2 + 2	2	6	1	11	$S_4\times C_2$ (as 6T11)	$ [8/3, 8/3, 3]_{3}^{2}$
2.6.11.13	x^6 + 10	2	6	1	11	$D_{6}$ (as 6T3)	$ [3]_{3}^{2}$
2.6.11.14	x^6 + 2x^4 + 10	2	6	1	11	$S_4\times C_2$ (as 6T11)	$ [4/3, 4/3, 3]_{3}^{2}$
2.6.11.15	x^6 + 2x^4 + 2x^2 + 10	2	6	1	11	$S_4\times C_2$ (as 6T11)	$ [8/3, 8/3, 3]_{3}^{2}$
2.6.11.16	x^6 + 2x^2 + 10	2	6	1	11	$S_4\times C_2$ (as 6T11)	$ [8/3, 8/3, 3]_{3}^{2}$
2.6.11.2	x^6 + 6x^4 + 14	2	6	1	11	$S_4\times C_2$ (as 6T11)	$ [4/3, 4/3, 3]_{3}^{2}$
2.6.11.3	x^6 + 2x^2 + 14	2	6	1	11	$S_4\times C_2$ (as 6T11)	$ [8/3, 8/3, 3]_{3}^{2}$
2.6.11.4	x^6 + 6x^4 + 4x^2 + 4x + 14	2	6	1	11	$S_4\times C_2$ (as 6T11)	$ [8/3, 8/3, 3]_{3}^{2}$
2.6.11.5	x^6 + 6	2	6	1	11	$D_{6}$ (as 6T3)	$ [3]_{3}^{2}$
2.6.11.6	x^6 + 6x^4 + 6	2	6	1	11	$S_4\times C_2$ (as 6T11)	$ [4/3, 4/3, 3]_{3}^{2}$
2.6.11.7	x^6 + 2x^2 + 6	2	6	1	11	$S_4\times C_2$ (as 6T11)	$ [8/3, 8/3, 3]_{3}^{2}$
2.6.11.8	x^6 + 4x^4 + 2x^2 + 6	2	6	1	11	$S_4\times C_2$ (as 6T11)	$ [8/3, 8/3, 3]_{3}^{2}$
2.6.11.9	x^6 + 6x^4 + 2	2	6	1	11	$D_{6}$ (as 6T3)	$ [3]_{3}^{2}$